I suppose it depends on what you’re including. If this truly is the reception-only budget, and you include flowers/decorations, photography, videography, transportation, attire, etc. in the ceremony budget, then it would be challenging but possible.
Remember taxes, too–I don’t know what Chicago’s tax rate is, but the $5000 venue would be more like $5350 (if it’s 7% tax.) You could make it work with a breakdown like this:
Grand Piazza–$3600 rental fee (~$3860 with taxes)
Rentals–if the room rental fee doesn’tinclude tables, chairs, and linens, you’ll need to rent these things. In my city, the going rate is ~$6-10/table, ~$2-4/chair, ~$2-4/tablecloth, and ~$1-$3/napkin, so assuming Chicago’s toward the more expensive end, that’ll come to around (again, very rough estimate) $1200 with taxes
DJ– ~$1500ish (I imagine that’s about what it would cost for a not high-end DJ including taxes…you could also skip the DJ and do an ipod playlist instead, save the $$)
Centerpieces, escort cards, any other reception decoration “stuff” you need–aiming for $300-400 total should be possible
So…with a budget of $15,000, if you go with the cheapest venue, rentals are included, you do ipod DJ and very minimal decorations, you’d have roughly $72/person to play with for food. Most places require a 20-25% service charge (plus, again, taxes), so really it’s more like $55/person actual food and beverage cost. That’s enough for a casual meal, maybe anopen bar without preminum brands, and cake (provided you go a cheaper route with cake, like cupcakes or sheet cake.)
If you have to do rentals and you do a DJ and more elaborate decorations, then you might have more of a challenge, but with modest enough food it could be possible. Then you’d have ~$53/person for food, probably more like ~$40/person before service charge and taxes. For that, you might be able to get casual food and some kind of dessert but no open bar, or maybe a beer and wine bar with very modest food offerings.